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Abstract <p>In this paper, we develop a method for evaluation of critical stress of cracks based on the Griffith fracture criterion under assumption that the elastic behavior of the body is governed by the strain gradient elasticity (SGE) theory. We use SGE definition for Eshleby tensor of ellipsoidal inclusion and consider the penny-shaped crack as the particular case of spheroidal void. The generalized traction-free boundary conditions on the crack faces are satisfied in averaged sense for the case of shear load applied in the far-field. Based on numerical calculations of Eshelby tensor components, we show that size effect for critical stress predicted by SGE coincides with classical elasticity for relatively large cracks. Obtained results can be used for the validation of numerical solutions and stress based fracture criteria within SGE.</p>

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On Energy-based Methods for Evaluation of Critical Stress of Cracks in Isotropic Bodies with Strain Gradient Effects

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Y. O. Solyaev,
  • K. S. Golubkin,
  • K. A. Shelkov

摘要

Abstract

In this paper, we develop a method for evaluation of critical stress of cracks based on the Griffith fracture criterion under assumption that the elastic behavior of the body is governed by the strain gradient elasticity (SGE) theory. We use SGE definition for Eshleby tensor of ellipsoidal inclusion and consider the penny-shaped crack as the particular case of spheroidal void. The generalized traction-free boundary conditions on the crack faces are satisfied in averaged sense for the case of shear load applied in the far-field. Based on numerical calculations of Eshelby tensor components, we show that size effect for critical stress predicted by SGE coincides with classical elasticity for relatively large cracks. Obtained results can be used for the validation of numerical solutions and stress based fracture criteria within SGE.